1------------------------------------------------------------------------------
2--                                                                          --
3--                         GNAT RUNTIME COMPONENTS                          --
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5--                       G N A T . H E A P _ S O R T                        --
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32------------------------------------------------------------------------------
33
34package body GNAT.Heap_Sort is
35
36   ----------
37   -- Sort --
38   ----------
39
40   --  We are using the classical heapsort algorithm (i.e. Floyd's Treesort3)
41   --  as described by Knuth ("The Art of Programming", Volume III, first
42   --  edition, section 5.2.3, p. 145-147) with the modification that is
43   --  mentioned in exercise 18. For more details on this algorithm, see
44   --  Robert B. K. Dewar PhD thesis "The use of Computers in the X-ray
45   --  Phase Problem". University of Chicago, 1968, which was the first
46   --  publication of the modification, which reduces the number of compares
47   --  from 2NlogN to NlogN.
48
49   procedure Sort (N : Natural; Xchg : Xchg_Procedure; Lt : Lt_Function) is
50      Max : Natural := N;
51      --  Current Max index in tree being sifted. Note that we make Max
52      --  Natural rather than Positive so that the case of sorting zero
53      --  elements is correctly handled (i.e. does nothing at all).
54
55      procedure Sift (S : Positive);
56      --  This procedure sifts up node S, i.e. converts the subtree rooted
57      --  at node S into a heap, given the precondition that any sons of
58      --  S are already heaps.
59
60      ----------
61      -- Sift --
62      ----------
63
64      procedure Sift (S : Positive) is
65         C      : Positive := S;
66         Son    : Positive;
67         Father : Positive;
68
69      begin
70         --  This is where the optimization is done, normally we would do a
71         --  comparison at each stage between the current node and the larger
72         --  of the two sons, and continue the sift only if the current node
73         --  was less than this maximum. In this modified optimized version,
74         --  we assume that the current node will be less than the larger
75         --  son, and unconditionally sift up. Then when we get to the bottom
76         --  of the tree, we check parents to make sure that we did not make
77         --  a mistake. This roughly cuts the number of comparisions in half,
78         --  since it is almost always the case that our assumption is correct.
79
80         --  Loop to pull up larger sons
81
82         loop
83            Son := C + C;
84
85            if Son < Max then
86               if Lt (Son, Son + 1) then
87                  Son := Son + 1;
88               end if;
89            elsif Son > Max then
90               exit;
91            end if;
92
93            Xchg (Son, C);
94            C := Son;
95         end loop;
96
97         --  Loop to check fathers
98
99         while C /= S loop
100            Father := C / 2;
101
102            if Lt (Father, C) then
103               Xchg (Father, C);
104               C := Father;
105            else
106               exit;
107            end if;
108         end loop;
109      end Sift;
110
111   --  Start of processing for Sort
112
113   begin
114      --  Phase one of heapsort is to build the heap. This is done by
115      --  sifting nodes N/2 .. 1 in sequence.
116
117      for J in reverse 1 .. N / 2 loop
118         Sift (J);
119      end loop;
120
121      --  In phase 2, the largest node is moved to end, reducing the size
122      --  of the tree by one, and the displaced node is sifted down from
123      --  the top, so that the largest node is again at the top.
124
125      while Max > 1 loop
126         Xchg (1, Max);
127         Max := Max - 1;
128         Sift (1);
129      end loop;
130   end Sort;
131
132end GNAT.Heap_Sort;
133